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### Quantum Physics Homework

Photoelectric Effect

1. The threshold frequency of tin is 1.2 x 1015Hz. What is the threshold wavelength? What is the work function of tin? Ans: 250 nm; 4.97 eV
2. In number one, if 167 nm light falls on tin, what is the kinetic energy of ejected photoelectrons? Ans: 2.47 eV
3. In number one, what is the speed of the ejected photoelectrons? Ans: 9.31 x 105 m/s
4. The threshold frequency of a given metal is 6.7 x 1014Hz. It is illuminated by 350 nm light. What is the kinetic energy of the ejected photoelectrons? Ans: 0.78 eV
5. In number four, the metal is illuminated by 550 nm light. What is the kinetic energy of the ejected photoelectrons? Ans: 0 eV
6. The work function of iron is 4.7 eV. What is the threshold wavelength of iron? Ans: 264 nm
7. If the iron is exposed to 150 nm light, what is the kinetic energy of the ejected electrons? Use work function of iron given in number 6. Ans: 3.58 eV
8. In number 7, what is their speed? Ans: 1.12 x 106m/s

de Broglie Wavelength

1. What is the de Broglie wavelength of a deuteron of mass 3.3 x 10-27kg that moves with a speed of 2.5 x 104m/s. Ans: 8.03 x 10-12m
2. What is the de Broglie wavelength of a proton (mass=1.67 x 10-27kg) moving at 1 x 106m/s? Ans: 3.97 x 10-13m
3. An electron is accelerated across a potential difference of 54 V. Find the maximum velocity of the electron. Ans: 4.36 x 106m/s
4. What is the de Broglie wavelength of the electron in number three? Ans: 1.67 x 10-10m
5. The kinetic energy of an electron is 13.65 eV. Find the velocity of the electron. Calculate its de Broglie wavelength. Ans: 2.19 x 106m/s; 0.332 nm
6. An electron has a de Broglie wavelength of 400 nm. What is its velocity? Ans: 1,818 m/s

Atomic Models

1. An electron in a mercury atom drops from 8.82 eV to 6.67 eV above its ground state. What is the energy of the photon emitted? What is its frequency? Ans: 2.15 eV; 5.19 x 1014Hz
2. What energy is associated with the second, third, fourth, fifth, and sixth energy levels in the hydrogen atom? Ans: -3.4 eV; -1.51 eV; -0.85 eV; -0.54 eV; -0.38 eV
3. Using the values calculated in number 2, determine the following energy differences for the hydrogen atom: E6 - E5 and E5 - E3. Ans: 0.16 eV; 0.97 eV
4. Using the values calculated in number three, determine the frequencies of light emitted by the photon given off in the energy changes. Ans: 3.86 x 1013Hz; 2.34 x 1014Hz
5. Determine the wavelengths of the emitted photons in number four. Ans: 7772 nm; 1282 nm